*The official ship name is a play on Haagen Dazs
WARNING: THIS DISCUSSION CONTAINS HEAVY SPOILERS.
I finished the drama the day the last episode aired, and I haven't watched it again. However, I did read most of the book. If you didn't know already, Yan Da is an original character from the drama, so she doesn't exist in the book.
In my opinion, it was unrealistic for Ying Kong Shi to have feelings for Yan Da (at least in season 1), because his cold and ruthless personality prevented him from having emotional attachment.
Let's look back at his childhood.
Ying Kong Shi's past life and his birth were destined to be a tragedy. In the book, Lian Ji/Lotus created him with magic just to use him as a pawn. He was created using a sleet bird feather, red lotus petal, and cherry blossom petal. In the drama, Ying Kong Shi had been discriminated by his "father", who never loved Lian Ji. He was bullied and discriminated by his older half-siblings because he couldn't use magic, and the only person that treated him with kindness was Ka Suo. Shi did not care for any of his siblings that died in the Second Ice and Fire War. Furthermore, the Ice King even chose Shi to be sacrificed for the Deicide Sword!
Shi's harsh childhood had shaped his personality. He did not trust anyone other than Ka Suo and probably his mom. He wanted to become king so he could protect his brother. He killed anyone that got in his way or threatened Ka Suo's happiness. He took advantage of anyone that helped him.
That is where Yan Da's specialty comes in. Shi likes her as an individual, but only to a certain extent. Shi is able to relate himself to her because they had a similar childhood. Although he pretended to be a loyal servant, he still proved that she was different from others. Remember how he ordered Liao Jian to release her from imprisonment in the Bear Tribe, even though he could have just walked away and left her tortured there? And when she was caught as a spy in the City of Bladed Snow, not only did he let her go and not expose her, he also allowed her to hit him, not something that he would tolerate in normal circumstances. Also, he listened to Yan Da when she begged him not to kill her father. Shi had a soft spot for her.
WARNING: DO NOT READ FURTHER UNLESS YOU HAVE WATCHED EPISODE 62.
Having to choose between her family and Ying Kong Shi, she betrayed the Fire Tribe several times, but that was not enough to win his heart. Even during her last moments where she asked him whether he ever liked her, he friendzoned her. I was angry at first, but I thought it through now. Shi's cold and ruthless personality prevented him from having emotional attachment, so how can he have romance when he was blinded by bromance? To regard Yan Da as his "only friend" throughout the story was a big win. Out of all those people, he only trusted Yan Da, an enemy of Ka Suo. Calling her a friend meant that she had a very important place in his heart, placed under Ka Suo and Lian Ji. She taught Ying Kong Shi how to love. She taught him friendship. Those feelings may turn into romance one day, if only she was still alive.
So if you really hope to see their love blossom, then look forward to the modern day sequel, Ice Fantasy Destiny :D